The Theoretical Regularity Properties of the Normalized Quadratic Consumer Demand Model

Barnett, William A. and Usui, Ikuyasu (2006): The Theoretical Regularity Properties of the Normalized Quadratic Consumer Demand Model.

Abstract

We conduct a Monte Carlo study of the global regularity properties of the Normalized Quadratic model. We particularly investigate monotonicity violations, as well as the performance of methods of locally and globally imposing curvature. We find that monotonicity violations are especially likely to occur, when elasticities of substitution are greater than unity. We also find that imposing curvature locally produces difficulty in the estimation, smaller regular regions, and the poor elasticity estimates in many cases considered in the paper. Imposition of curvature alone does not assure regularity, and imposing local curvature alone can have very adverse consequences.

• Item Type: MPRA Paper
• Language: English
• Keywords: Monte Carlo; flexible functional form; production; normalized quadratic; regularity; curvature; monotonicity
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C30 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General

References

Arrow, K. J. and Enthoven, A. C. (1961). Quasi-concave programming. Econometrica 29, 779-800.

Barnett, W. A. (1983a). New indices of money supply and the flexible Laurent demand system. Journal of Business and Economic Statistics 1, 7-23 (Reprinted in The Theory of Monetary Aggregation, W. A. Barnett and A. Serletis (eds.), 2000, Chapter 16. Elsevier: North-Holland).

Barnett, W. A. (1983b). Definitions of second order approximation and of flexible functional form. Economics Letters, 12, 31-35 (Reprinted in Functional Structure and Approximation in Econometrics, W. A. Barnett, and J. M. Binner (eds.), 2004, Chapter 3, Amsterdam, Elsevier).

Barnett, W. A. (2002). Tastes and technology: curvature is not sufficient for regularity. Journal of Econometrics, 108, 199-202 (Reprinted in Functional Structure and Approximation in Econometrics, W. A. Barnett, and J. M. Binner (eds.), 2004, Chapter 17, Amsterdam, Elsevier).

Barnett, W. A. and Choi, S. (1989). A Monte Carlo study of tests of blockwise weak separability. Journal of Business and Economic Statistics 7, 363-377 (Reprinted in Functional Structure and Approximation in Econometrics, W. A. Barnett, and J. M. Binner (eds.), 2004, Chapter 12, Amsterdam, Elsevier).

Barnett, W. A. and Jonas, A. (1983). The Müntz-Szatz demand system: an application of a globally well behaved series expansion. Economics Letters, 11, 337-342 (Reprinted in Functional Structure and Approximation in Econometrics, W. A. Barnett, and J. M. Binner (eds.), 2004, Chapter 8, Amsterdam, Elsevier).

Barnett, W. A. and Lee, Y. W. (1985). The global properties of the minflex Laurent, generalized Leontief, and translog flexible functional forms. Econometrica, 53, 1421-1437 (Reprinted in Functional Structure and Approximation in Econometrics, W. A. Barnett, and J. M. Binner (eds.), 2004, Chapter 4, Amsterdam, Elsevier).

Barnett, W. A. and Pasupathy, M. (2003). Regularity of the generalized quadratic production model: a counterexample. Econometric Review 22(2), 135-154.

Barnett, W. A., Geweke, J. and Wolfe, M. (1991a). “Semiparametric Bayesian estimation of applied general equilibrium models,” in Equilibrium Theory and Applications, Proceedings of the Sixth International Symposium in Economic Theory and Econometrics, W. A. Barnett, A. Mas-Colell, J. Drèze, C. D’Aspremont and B. Cornet (eds.), Cambridge, MA: Cambridge University Press, 425-480.

Barnett, W. A., Geweke, J. and Wolfe, M. (1991b). Semiparametric Bayesian estimation of the asymptotically ideal production model,” Journal of Econometrics, 49, 5-50 (Reprinted in Functional Structure and Approximation in Econometrics, W. A. Barnett, and J. M. Binner (eds.), 2004, Chapter 14, Amsterdam, Elsevier).

Barnett, W. A., Kirova, M. and Pasupathy, M. (1995). Estimating policy invariant deep parameters in the financial sector when risk and growth matter. Journal of Money, Credit and Banking 27, 1402-1430 (Reprinted in The Theory of Monetary Aggregation, W. A. Barnett, and A. Serletis (eds.), 2000, Chapter 22, North Holland).

Barnett, W. A., Lee, Y. W. and Wolfe, M. D. (1985). The three-dimensional global properties of the Minflex Laurent, generalized Leontief, and translog flexible functional forms. Journal of Econometrics, 30, 3-31 (Reprinted in Functional Structure and Approximation in Econometrics, W. A. Barnett, and J. M. Binner (eds.), 2004, Chapter 6, Amsterdam, Elsevier).

Barnett, W. A., Lee, Y. W. and Wolfe, M. D. (1987). The global properties of the two Minflex Laurent flexible functional forms. Journal of Econometrics, 36, 281-298 (Reprinted in Functional Structure and Approximation in Econometrics, W. A. Barnett, and J. M. Binner (eds.), 2004, Chapter 7, Amsterdam, Elsevier).

Barten, A. P. (1969). Maximum likelihood estimation of a complete system of demand equations. European Economic Review 1, 7-73.

Basmann, R. L., Molina, D. J. and Slottje, D. J. (1983). Budget constraint prices as preference changing parameters of generalized Fechner-Thurstone direct utility functions. American Economic Review 73(3), 411-413.

Basmann, R. L., Fawson, C. and Shumway, R. C. (1990). Agricultural production technologies with systematic and stochastic technical change. American Journal of Agricultural Economics 72(1), 182-199.

Basmann, R. L., Hayes, K. J. and Slottje, D. J. (1994). Testing an alternative habit persistence model. Southern Economic Journal 60(3), 739-753.

Basmann, R. L., Diamond, C. A., Frentrup, J. C. and White, S. N. (1985). On deviations between neoclassical and GFT-based true cost-of-living indexes derived from the same demand function system. Journal of Econometrics 30, 45-66 (Reprinted in New Approaches to Modeling, Specification Selection, and Econometric Inference, W. A. Barnett, and A. R. Gallant (eds.), 1989, Cambridge University Press, Cambridge, 45-66).

Berndt, E. R. and Khaled, M. S. (1979). Parametric productivity measurement and choice among flexible functional forms. Journal of Political Economy 87(6), 1220–1245.

Blackorby, C., Primont, D. and Russell, R. R. (1977). On testing separability restrictions with flexible functional forms. Journal of Econometrics 5, 195-209.

Blackorby, C. and Russell, R. R. (1989). Will the real elasticity of substitution please stand up? (A comparison of the Allen/Uzawa and Morishima elasticities). American Economic Review 79, 882-888.

Caves, D. W. and Christensen, L. R. (1980). Global properties of the flexible functional forms. American Economic Review 70, 422-432.

Christensen, L. R., Jorgenson, D. W. and Lau, L. J. (1971). Transcedental logarithmic production frontiers. Review of Economics and Statistics 55, 28-45.

Deaton, A. and Muellbauer, J. (1980). An almost ideal demand system. American Economic Review 70, 312-326.

Diewert, W. E. (1971). An application of the Shephard duality theorem: a generalized Leontief production function. Journal of Political Economy 79, 481-507.

Diewert, W. E. (1974). “Applications of duality theory,” in Frontiers of Quantitative Economics, M. D. Intriligator and D. A. Kendrick (eds.), vol. 2, Amsterdam: North-Holland, 106-171.

Diewert, W. E. and Wales, T. J. (1987). Flexible functional forms and global curvature conditions. Econometrica 55, 43-68.

Diewert, W. E. and Wales, T. J. (1988a). A normalized quadratic semiflexible functional form. Journal of Econometrics 37, 327-342.

Diewert, W. E. and Wales, T. J. (1988b). Normalized quadratic systems of consumer demand functions. Journal of Business and Economic Statistics 6, 303-312.

Diewert, W. E. and Wales, T. J. (1992). Quadratic spline models for producer supply and demand functions, International Economic Review 33, 705-722.

Diewert, W. E. and Wales, T. J. (1993). Linear and quadratic spline models for consumer demand Functions. Canadian Journal of Economics 26, 77-106.

Diewert, W. E. and Wales, T. J. (1995). Flexible functional forms and tests of homogeneous separability. Journal of Econometrics 67, 259-302.

Diewert, W. E. and Fox, K. J. (1999). “Is the Asia-pacific region different? Technical progress bias and price elasticity estimates for 18 OECD countries, 1960-1992,” in Economic Efficiency and Productivity Growth in the Asia-Pacific Region, T-T. Fu, C. J. Huang and C. A. K. Lovell (eds.), Cheltenham and Northampton, UK: Edward Elgar Publishing, 125-144.

Dorsey, R. E. and Mayer, W. J. (1995). Genetic algorithms for estimation problems with multiple optima, nondifferentiability, and other irregular features. Journal of Business and Economic Statistics 13, 53-66.

Fleissig, A. R., Kastens, T. and Terrell, D. (2000). Evaluating the semi-nonparametric Fourier, AIM, and neural networks cost functions. Economics Letters 68, 235-244.

Gallant, A. R. (1981). On the bias in flexible functional forms and an essentially unbiased form: the Fourier flexible form. Journal of Econometrics 1(5), 211-245.

Gallant, A. R. and Golub, G. H. (1984). Imposing curvature restrictions on flexible functional forms. Journal of Econometrics 267, 295-321.

Guilkey, D. K. and Lovell, C. A. K. (1980). On the flexibility of the translog approximation. International Economic Review 21, 137-147.

Guilkey, D. K., Lovell, C. A. K. and Sickles, R. C. (1983). A comparison of the performance of three flexible functional forms. International Economic Review 24, 591-616.

Hanoch, G. (1975). Production and demand model with direct and indirect implicit additivity. Econometrica 45, 395-419.

Humphrey, D. B. and Moroney, J. R. (1975). Substitution among capital, labor, and natural resource products in American manufacturing. Journal of Political Economy 83, 357-382.

Jensen, M. J. (1997). Revisiting the flexibility and regularity of the asymptotically ideal production model. Econometric Reviews 16, 179-203.

Kohli, U. (1993). A symmetric normalized quadratic GNP function and the U.S. demand for imports and supply of exports. International Economic Review 34, 243-255.

Lau, L. J. (1978), “Testing and Imposing Monotonicity, Convexity, and Quasiconcavity,” in Production Economics, A Dual Approach to Theory and Applications, M. Fuss and D. McFadden (eds.), vol. 1, Amsterdam: North-Holland, 409-453.

Manser, M. E. (1974). Estimating Consumer Preferences and Cost of Living Indexes for US Meat and Produce (1947-1971), Ph.D. Thesis, University of Wisconsin, Madison, USA.

Moschini, G. (1998). The semiflexible almost ideal demand system. European Economic Review 42, 349-364.

Ryan, D. L. and Wales, T. J. (1998). A simple method for imposing local curvature in some flexible consumer-demand systems. Journal of Business and Economic Statistics 16, 331-338.

Ryan, D. L. and Wales, T. J. (2000). Imposing local concavity in the translog and generalized Leontief cost functions. Economics Letters 6, 253-260.

Serletis, A. and Shahmoradi, A. (2005). Semi-nonparametric estimates of the demand for money in the United States. Macroeconomic Dynamics 9, 542-559.

Terrell, D. (1995). Flexibility and regularity properties of the asymptotically ideal production model. Econometric Review 14, 1-17.

Terrell, D. (1996). Incorporating monotonicity and concavity restrictions in flexible functional forms. Journal of Applied Econometrics 11, 179-194.

Uzawa, H. (1962). Production functions with constant elasticities of substitution. Review of Economics Studies 29, 129-299.

Wales, T. J. (1977). On the flexibility of flexible functional forms. Journal of Econometrics 5, 183-193.

White, H. (1980). Using least squares to approximate unknown regression functions. International Economic Review 21, 149-170.

Wiley, D. E., Schmidt, W. H. and Bramble, W. J. (1973). Studies of a class of covariance structure models. Journal of the American Statistical Association 68, 317-323.